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A tridiagonal matrix is a square matrix with zeroes everywhere except on the main diagonal and the diagonals just above and below the main diagonal.

Let $T$ be a real anti-symmetric tridiagonal matrix with elements $t_{12}=c_{1}, t_{23}=c_{2}, \ldots$, $t_{n-1 n}=c_{n-1}$. If $n$ is even, compute det $T$.
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